Calculus

Higher-order Derivatives

Characteristics of f, f', f''

         

Let ff be a function such that f(0)=50.f(0)=50. If the above graph represents the graph of the first derivative of ff on the interval 0<x<3,0<x<3, which of the following is the correct description of ff on this interval?

For the function y=x3+x2x1,y=x^3+x^2-x-1, determine the interval where yy is decreasing.

Suppose ff is a function such that f(0)=33f(0)=33 and the first derivative of ff on the interval 2<x<2-2 < x < 2 is as shown in the above diagram. Which of the following is the correct description of the function ff on this interval?

Suppose ff is a function defined on the closed interval 3x4-3 \le x \le 4 with f(0)=42,f(0)=42, such that the graph of f,f', the derivative of f,f, on the interval is as shown in the above diagram. On what intervals is ff increasing?

Suppose ff is a function defined on the closed interval 3x4-3 \le x \le 4 with f(0)=3f(0)=3 such that the graph of f,f', the derivative of f,f, on the interval is as shown in the above diagram. Find the xx-coordinates of the points of inflection of f.f.

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